Think you might be right. I booked it online with the 24 hour break, then called today and got it changed to the same day flight.
Very happy with the flights we were able to get in the end.
Melbourne -> Singapore Qantas in J
Singapore -> Tokyo on JAL in J then onwards to San Fran on JAL in premium economy.
San Francisco -> Cabo on Alaska economy
Bogota -> Athens via Madrid on Iberia in J
London -> Sydney via Bangalore on BA/Qantas in J
My advice to anyone trying to do this as a bronze frequent flyer like me is that the availability always seems to be better in the multi city search tool. Book your most important flights through that and just accept that you will have to cop the 5,000 points to make changes to add the flights you couldn't fit in the search over the phone.
Helped that when calling today was answered in less than minute by the Australian call centre, I think because I had the existing business booking?